Answer:
[tex]\boxed{3 \dfrac{7}{12}}[/tex]
Step-by-step explanation:
The first step in simplifying the expression is to convert both the fractions into improper fractions [a/b (a > b)].
⇒ [tex]7\dfrac{2}{8} - 3\dfrac{2}{3}[/tex]
⇒ [tex]\dfrac{7 \times 8 + 2}{8} - \dfrac{3 \times 3 + 2}{3}[/tex]
⇒ [tex]\dfrac{56 + 2}{8} - \dfrac{9 + 2}{3}[/tex]
⇒ [tex]\dfrac{58}{8} - \dfrac{11}{3}[/tex]
The next step in simplifying the expression is to make the denominators of both fractions equivalent.
⇒ [tex]\dfrac{58}{8} - \dfrac{11}{3}[/tex]
⇒ [tex]\dfrac{58 \times 3}{8 \times 3} - \dfrac{11 \times 8}{3 \times 8}[/tex]
⇒ [tex]\dfrac{174}{24} - \dfrac{88}{24}[/tex]
The third step in simplifying the expression is to subtract the fractions.
⇒ [tex]\dfrac{174}{24} - \dfrac{88}{24}[/tex]
⇒ [tex]\dfrac{86}{24}[/tex]
The fourth step in simplifying the expression is to simplify the difference of the two fractions.
⇒ [tex]\dfrac{86}{24}[/tex]
⇒ [tex]\dfrac{86 \div 2}{24 \div 2}[/tex]
⇒ [tex]{\dfrac{43}{12}}[/tex]
The fifth step in simplifying the expression is to convert the improper fraction into mixed fraction.
⇒ [tex]{\dfrac{43}{12}}[/tex]
⇒ [tex]{\dfrac{36}{12}} + \dfrac{7}{12}[/tex]
⇒ [tex]3 + \dfrac{7}{12}[/tex]
⇒ [tex]\boxed{3 \dfrac{7}{12}}[/tex]
